Yes, you can have your pet euthanized in your home. In my area, some vets will come to one's house when it's time for an elderly and/or sick pet to be euthanized and the owner would prefer not to put them through a stressful car ride. So I would start by calling up either your regular vet or vet clinics in your area. You should also inquire about how the remains are handled. If you live in a rural area, you probably have the option for a home-buriel. But in more urban areas there might be laws against it. If you're looking to have the pet cremated, then you need to decide if you don't want the ashes, or if you do want the ashes. If you do want the ashes, typically it's a separate company that does the cremation, so you'd need to find out if you need to call them to arrange for them to come to your house at the same time as the euthanization, or if the vets clinic takes the remains with them and then the pickup by the crematory company is at the vets.